#### Alladi Ramakrishnan Hall

#### Quantum uncertainty relation based on the mean deviation

#### Chiranjib Mukhopadhyay

##### HRI, Allahabad

*Traditional forms of quantum uncertainty relations invariably use the standard deviation based approach. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present an alternative form of uncertainty relation, in both state dependent and state independent form, based on the mean deviation. We illustrate the robustness of this formulation for situations where the standard deviation based uncertainty relation is inapplicable. We apply the mean deviation based uncertainty relation to detect EPR violation in a lossy scenario for a higher inefficiency threshold than that allowed by the standard deviation based approach. We demonstrate that the mean deviation based uncertainty relation can perform equally well as the standard deviation based uncertainty relation as non-linear witness for entanglement detection. We also derive a quantum speed limit for unitary evolution based on the mean deviation based uncertainty relation - which although weaker than the existing bounds, suggest an intriguing bridge between the average energy based speed limits and variance based speed limits in literature.*

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